In the spectrum of hydrogen atom, the ratio of the longest wavelength in Lyman series to thelongest wavelength in the Balmer series is

The transition from the state $n = 4$ to $n = 3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition

In the Rutherford's nuclear model of the atom, the nucleus (radius about $10^{-15} \;m$ ) is analogous to the sun about which the electron move in orbit (radius $\approx 10^{-10} \;m$ ) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than actually it is? The radius of earth's orbit is about $1.5 \times 10^{11} \;m.$ The radius of sun is taken as $7 \times 10^{8}\;m$

Give the relationship between impact parameter and scattering angle. 

Show the trajectory of $\alpha -$ particle of different impact parameter and using it how did Rutherford determine the upper limit of the nuclear size ? 

The number of completely filled shells for the element ${ }_{16} S ^{32}$ is